Iterative solution of nonlinear equations involving strongly accretive operators without the Lipschitz assumption (Q1378390)

Let \(E\) be a real Banach space with a uniformly convex dual space \(E^*\). Suppose \(T: E\to E\) is a continuous (not necessarily Lipschitzian) strongly accretive map such that \((I- T)\) has bounded range, where \(I\) denotes the identity operator. It is proved that the Ishikawa iterative sequence converges strongly to the unique solution of the equation \(Tx= f\), \(f\in E\).